The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts. The Mathematical Monthly - Page 101859Full view - About this book
| James Hodgson - Astronomy - 1723 - 724 pages
...t,¿z¿xct,í7<r— Axes, bac; that is the Radius multiplied into the Sine of the Complement of the Angle a or Sine of the Middle Part, is equal to the Product of the Tangent of ab one of the Extreams, into the Tangent of the Complement of л с the other Extream. By... | |
| Euclid, John Keill - Geometry - 1733 - 444 pages
...S, CF=Cof. BC and T, DF = Cot. B. Wherefore R x Cof. BC=Cot. Cx Cot. B ; that is, Radius drawn into the Sine of the. middle Part, is equal to the Product of the Tangents of the adjacent extreme Parts. : X And And BA, AC, are the oppofite Extremes to the faid middle... | |
| Mathematics - 1801 - 658 pages
...solutions of all the cases of right-angled spherical triangles. THEOREM VII. The product of radius and the sine of the middle part is equal to the product of the tangents of the conjunct extremes, or to that of the cosines of the disjunct extremes.* NOTE. * DEMONSTRATION.... | |
| Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...parts are to be computed by the two following equations ; viz., 1st. — The product of radius and the sine of the middle part, is equal to the product of the tangents of the extremes conjunct2d. — The product of radius and the sine of the middle part, is... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...; and the other two parts are called the opposite parts. The two theorems are as follows. (474) I. The sine of the middle part is equal to the product of the tangents of the two adjacent parts. (475) II. The sine of the middle part is equal to the product of... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...; and the other two parts are called the opposite parts. The two theorems are as follows. (474) I. The sine of the middle part is equal to the product of the tangents of the two adjacent parts. (475) II. The sine of the middle part is equal to the product of... | |
| Henry W. Jeans - Trigonometry - 1842 - 138 pages
...= cos- P/=cos. co. A. CP C/P/ PN P/N, tan. A = — = = cot. P,= cot. co. A Are. CN C,N, Gl RULE I. The sine of the middle part is equal to the product of the tangents of the two parts adjacent to it. RULE II. The sine of the middle part is equal to the product... | |
| Matthew Fontaine Maury - Navigation - 1843 - 458 pages
...part, and certain trigonometric functions of the extremes. They are, § 165. The product of radius and sine of the middle part, is equal to the product of the tangents of extremes conjunct. And, § 166. The product of the co-sines of extremes disjunct, is equal... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...the other two parts are called the opposite parts. The two theorems are as follows. Napier's Rules. II. The sine of the middle part is equal to the product of the cosines of the two opposite parts. [B. p. 436.] Proof. To demonstrate the preceding rules, it is only necessary to... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...the other two parts are called the opposite parts. The two theorems are as follows. Napier's Rules. II. The sine of the middle part is equal to the product of the cosines of the two opposite parts. [B. p. 436.] Proof. To demonstrate the preceding rules, it is only necessary to... | |
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